Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <stack>
using namespace std;

typedef long long ll;
typedef pair<int, int> P;

#define pb push_back
#define rep(i, a, n) for(int i = (a); i < (n); i++)
#define dep(i, a, n) for(int i = (a); i >= (n); i--)
#define mod 1e9+7

int main() {
  int n;
  cin >> n;
  double a[1000];
  rep(i, 0, n) cin >> a[i];
  sort(a, a + n);
  double s1 = (a[n - 3] + a[n - 4]) / (a[n - 1] - a[n - 2]);
  double s2 = (a[n - 1] + a[n - 4]) / (a[n - 2] - a[n - 3]);
  double m = 1145141919;
  rep(i, 0, n - 2) m = min(m, a[i + 1] - a[i]);
  cout << fixed << max((a[n - 1] + a[n - 2]) / m, max(s1, s2)) << endl;
}